Calculating Nonlinearity of Boolean Functions with Walsh-Hadamard Transform – B-sides

http://konukoii.com/blog/2016/06/30/calculating-nonlinearity-of-boolean-functions-with-walsh-hadamard-transform/

Even simpler presentation

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http://www.tcs.hut.fi/Studies/T-79.5501/2007SPR/lectures/boolean.pdf

Wish I’d known this before reading the tunny report.

At the same time, it’s fascinating to see how folks in 1940 arrived at the same theory
The rest of the series looks just as interesting.

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http://faculty.luther.edu/~macdonal/GA&GC.pdf

Why do physicists despise Clifford algebra?

Because it opens their field to a hundred million open minded computer science students, eager to unify.

Put Clifford algebra into the heart of year two cs math, its game over.

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Clifford Algebra: A visual introduction – slehar

https://www.google.com/amp/s/slehar.wordpress.com/2014/03/18/clifford-algebra-a-visual-introduction/amp/

Sunday reading. So well written

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Easy stats

http://www.math.uah.edu/stat/expect/Properties.html

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simplex geometry

http://www.umsl.edu/~fraundorfp/ifzx/simplexGeometry.html

How I’ve been thinking of the fano plane

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http://www.math.vt.edu/people/brown/doc/731.pdf

Wish there were more papers written like this!

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Linear transformations and norm – Mathematics Stack Exchange

http://math.stackexchange.com/questions/21429/linear-transformations-and-norm

Turing’s fbar is 1

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http://www.dhcs.ca.gov/services/ccs/cmsnet/Documents/thiscomputes155.pdf

Second opinion rules ;in ca) nv won’t be much different

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http://www1.spms.ntu.edu.sg/~frederique/lecture9ws.pdf

Page 14 is almost exact Turing

Now we know why!

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http://www.math.cornell.edu/~dcollins/math4310/QuotientVectorSpaces.pdf

Excellent intuitions about why for Gilbert spaces and field embedding one is interested in constant functions on cosets.

Contrasts nicely with the stats motivation that is the background to the (colossus aided) counting attack on Tunny cipher (and certain aspects of enigma too)

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House intel committee: Partisan split over canceled open hearing – CNNPolitics.com

http://www.cnn.com/2017/03/24/politics/devin-nunes-paul-manafort-house-intelligence/index.html

So does a us president have the power and/or authority to “arrange” for the @incidental collection” of every collectible communication of us person #99?

Yes.

And yes gchq assist is that @arrangement”

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StarWind V2V Converter – Free Tool from StarWind! – Starwindsoftware.com

https://www.starwindsoftware.com/converter

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https://arxiv.org/pdf/1504.04885.pdf

Quaternion formalism and physics, 1880-1940

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Averaging

Does the action of the averaging operator factorize the dimension of the wheel in to the substances of the wheel writings?

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Colossus c(l) osets vs statistics

It’s now clear to me that while good et al thought of the attack on tunny in purely statistical theory, Newman and Turing thought of it in terms of topology (and log linear multinomials)

We have yet to see a Newman/Turing analysis (or topology applied to either enigma or tunny (or Italian heybern)) yet.

I see why it would still be seen as sensitive.

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Metadata on trump

When I wrote my last memo I didn’t know that it was part of a wider maelstrom.

It’s clear that the Truisms of all American (cum British) lying are abound; with definitional lying at the fore.

In my Era, pre 911, via 2 layers of Anglo-American (unofficially well coordinated) small contractors, each agency would have the other (small contractor) do metadata collection (on each other’s citizens)

This all went away post 911, when each agency could do it officially (whereas before metadata was legally grey)

What was retained, post 911, was the apparatus of grey ness.

Beware trump, with his CIA and NSA versions of his preatorian guards. Now beholden to the new emporer, the old guard may be lynched; Such is the nature of raw naked (super secret) power.

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Gchq spying on trum

“based on the information available to us, we see no indications that Trump Tower was the subject of surveillance by any element of the United States government either before or after Election Day 2016.”

As I recall when deniability is required, that’s when NSA induced gchq to do the spying on Americans (contact with foreign targets, of course)

Trump must be up by now on how and what NSA do!?

He won’t be as adept as Obama. But give him time. The absolute power of secret spying will either tame his dictatorial impulses or get him rapidly impeached.

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Turings on permutations focus on mean = 1

Finally I understand the meaning of the mean being 1.

Id figured a while ago that he was interested in the shuffle around 1.

But now we get that in eigenvector explanation (which is better than the shuffle!)

any distribution is the sum of 1/n of the 1 eigenvector + a superposition of weighted others.

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Constant functions, in Turing op paper

http://www.stat.uchicago.edu/~pmcc/reports/quotient.pdf

Professional version of my similar drivel at https://yorkporc.wordpress.com/2013/10/10/turings-quantum-of-informationa-typex-wheel-wiring-plan-predating-shannons-information-theory/

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https://www.maths.tcd.ie/pub/Maths/Courseware/GroupRepresentations/FiniteGroups.pdf

One d reps of groups , per Turing almost exactly

here

This is the second paper with modern presentation of two of the argumentation devices Turing used in on permutations. First we finally understand the why of wanting to establish that the math power of d generator is always positive 1. And second, we see why his lemma a is concerned with a power of four.

See paper for other examples of both argumentation devices.

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https://www.math.u-psud.fr/~breuilla/part0gb.pdf

See 1.3

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CiteSeerX — GROUP THEORY IN CRYPTOGRAPHY

http://citeseerx.ist.psu.edu/viewdoc/summary;jsessionid=349DB81FF478DC49989540C68EAE06EF?doi=10.1.1.249.1882

see 3.4 log signature s

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Ewens distribution on the symmetric group – Groupprops

https://groupprops.subwiki.org/wiki/Ewens_distribution_on_the_symmetric_group

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on permutations and lie algebras

if we reanalyze turings final argument can we say that he is testing for a given representation being one that is a group, given a lie algebra and its generator?  

he really says that g has subgroup h which inturn has a centralizer subgroup h1
see http://www.turingarchive.org/viewer/?id=133&title=29

see also k:

Generalization to Borel setsEdit

This distribution can be generalized to more complicated sets than intervals. If S is a Borel set of positive, finite measure, the uniform probability distribution on S can be specified by defining the pdf to be zero outside S and constantly equal to 1/K on S, where K is the Lebesgue measure of S

from https://en.m.wikipedia.org/wiki/Uniform_distribution_(continuous)

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The PDF for Lie groups and algebras for physicists

https://www.liealgebrasintro.com/publications
let me see two turing arguments

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developing from basics

http://www.complex-systems.com/pdf/05-4-3.pdf

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eigenvalues of random matrices. turings kernel K

image

https://case.edu/artsci/math/esmeckes/Haar_notes.pdf

i like this writer. she doesnt lose the point with endless symbols.

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lovely Turing mixer theory

https://www.cs.princeton.edu/courses/archive/fall13/cos521/lecnotes/lec12.pdf

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Accumulation Point — from Wolfram MathWorld

http://mathworld.wolfram.com/AccumulationPoint.html
this is the sense of turing- the point at which the measure of diffusion (of colinear differentials in crypto) has become chaotic

recall turing used a doubly transitive operator to mix the plaintext differentials within the output space

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